Question

A Ferris wheel is 45 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes.
The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t).

Answer 1

Answer:

- If the wheel rotates clockwise, the height function is

h(t) = 28.5 + 22.5sin(270 - 36t)

- If the wheel rotates anticlockwisely, the high function is

r(t) = 28.5 + 22.5sin(270 + 36t)

Step-by-step explanation:

- Centre line of the function

h = f(t)

= the height of the center of the ferris wheel

= 6 + 45/2 = 6 + 22.5 = 28.5 meters.

- The period of rotation is 10 minutes; so the wheel turns 360/10 = 36 degrees per minute.

It is not clearly stated if the wheel rotates clockwise or anti-clockwise.

Let us consider both cases:

- If it rotates clockwise, the current angle is a = 270 - 36t degrees, where t is the time in minutes.

Then the height function h = f(t)

= 28.5 + 22.5sin(a)

= 28.5 + 22.5sin(270 - 36t)

- If the wheel rotates anti-clockwise, the current angle is

b = 270 + 36t degrees.

Then the height function

h = r(t)

= 28.5 + 22.5sin(b)

= 28.5 + 22.5sin(270 + 36t)